Silly Syllogism?
If it’s raining, the game is canceled. It is raining. So the game is canceled.
What is modus ponens? (Valid)
This is the contradictory of “All dogs are loyal”.
What is "Some dog is not loyal"?
"Professor Whitley has written a long op-ed arguing that the university should keep its tenure system. Well, she has tenure, so I’m not sure what we expected."
Circumstantial ad hominem
Alice didn't go to the party if Bob did. Bod did go. It follows that...
Alice didn't go.
Rule: “The alarm sounds and the light flashes.” The alarm sounds, but the light doesn’t flash. Is the rule true or false?
False
Bob studied only if he passed. And Bob did pass. So Bob studied.
What is affirming the consequent? (Invalid)
This is the contradictory of “It is necessary that P”?
What is "It is permissible that not P"?
"Carlos says the dining hall should offer a vegetarian option every night. But I don’t think we should force every student on campus to give up meat."
What is the straw man fallacy?
Alice is happy unless Bob isn't sad. And we know that Bob is sad. It follows that...
Alice is happy.
Rule: “Bob brings chips or Alice brings salsa.” Both of them bring their items. Is the rule true or false?
True
The airport terminal has a cafe or a restaurant. And it does have a restaurant. Thus the terminal doesn't have a cafe.
What is affirming a disjunct? (Invalid)
or...
What is affirming the consequent? (Invalid)
Assuming there are senators, if "Some senators are lawyers" is false, then this is the truth value of "Some senators are not lawyers."
What is true?
“Critics say the Hollis Museum’s new admission fee prices out low-income families. But what counts as ‘low income’? $30,000 a year? $40,000? $50,000? Who knows? The complaint thus doesn’t really make sense.”
Line drawing fallacy
Alice is happy only if Bob is at the store. Bob is at the store only if Carlos is at the movies. It follows that, if Alice is happy, then...
Carlos is at the movies.
Rule: “If you park in Lot C, you have a permit.” Carlos doesn’t park in Lot C and has no permit. Did he break the rule?
No
The concert doesn't go on unless it doesn't storm. It stormed. So the concert didn’t go on.
What is disjunctive syllogism? (Valid)
This sentence is the contrary of "It is necessary that you park in Lot A".
What is "It is necessary that you not park in Lot A"?
“Originalists hold that the meaning of a constitutional amendment is fixed by its original public meaning. But ear-cropping was a common punishment when the 8th Amendment was ratified, so an originalist can't say such punishment is "cruel and unusual." The general problem is that many amendments were written a long time ago, before important developments in how we think about morality."
What is the genetic fallacy?
Bob won't lend Alice his car only if she doesn't fill the tank. Since we know Alice did fill the tank, it follows that...
Bob will lend Alice his car.
Rule: “The light goes on only if there’s a quarter in the machine.” Which situation breaks the rule?
No quarter, but the light goes on
Since Bob's GPA is not above 3.5, he won't get the scholarship. After all, Bob will get the scholarship only if his GPA is above 3.5.
What is modus tollens? (valid)
The sentence "It's not necessary that not P" is logically equivalent to this corner of the modal square of opposition.
What is the bottom left square?
"Some powerful AI companies are urging Congress to force AI development to slow down, in order to ensure appropriate safeguards are in place. But I think it's more plausible to hold that this is instead a cynical way for these companies to stifle competition."
What is a false dilemma?
Alice will get the internship only if she aces the interview. Bob’s helping her prepare is necessary for Alice to ace the interview. It follows that...
If Alice got the internship, then Bob helped her prepare.
Rule: “The machine dispenses a snack if and only if you press the button.” Which two situations make the rule false?
You press the button and get no snack. You don’t press the button and get a snack.